# Full text of "Analytical Mechanics"

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```ADDITION AND RESOLUTION OF VECTORS            7
Thus the magnitude of c equals the algebraic sum of the magnitudes of a and b, while its direction is the same as that of the larger of the two. It is evident that if the magnitudes of a and b are equal c vanishes. Therefore two vectors of equal magnitude and opposite directions are the negatives of each other. In other words, when the direction of a vector is reversed its sign is changed.
(c) When a and b are at right angles to each other, as in
Fig. 6c, <t> = 5 -    Therefore
and                           tan 6 = - -
a
12. Difference of Two Vectors. — Subtraction is equivalent to the addition of a negative quantity. Therefore, to subtract b from a we add — b to a. Thus we .have the following rule for subtracting one vector from another.
In order to subtract one vector from another reverse the one to be subtracted and add it to the other vector.
It is evident from Fig. 7 that the sum and the difference of two vectors form the diagonals of the parallelogram, determined by them.
ILLUSTRATIVE EXAMPLES.
A particle is displaced 10 cm. N. 30° E., then 10 cm. E. Find the resulting displacement.
Representing the displacements and their resultant by the vectors a, b, and c, Fig. 8, we obtain
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